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Popular >

extreme f(x)=1+1/x-1/(x^2)

Solution

extreme points

f (x) = 1 + \frac{1}{x} - \frac{1}{x ^{2}}

Solution

Maximum (2, \frac{5}{4})

Solution steps

f^{'} (x) = \frac{2}{x ^{3}} - \frac{1}{x ^{2}}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 2

into

1 + \frac{1}{x} - \frac{1}{x ^{2}} : \frac{5}{4}

Maximum (2, \frac{5}{4})

Popular Examples

extreme f(x)=x^{1/5}(x+3)extreme points

f (x) = x^{\frac{1}{5}} (x + 3)

extreme x^3+3x^2+1 extreme points

x^{3} + 3 x^{2} + 1

extreme f(x)=-5x^4+5x^3-10 extreme points

f (x) = - 5 x^{4} + 5 x^{3} - 10

extreme f(x,y)=3x^{-2}+5y^{-2}+8xy^2 extreme points

f (x, y) = 3 x^{- 2} + 5 y^{- 2} + 8 x y^{2}

extreme f(x,y)=4x^4+4y^4-xy extreme points

f (x, y) = 4 x^{4} + 4 y^{4} - x y

Frequently Asked Questions (FAQ)

What is the extreme f(x)=1+1/x-1/(x^2) ?
The extreme f(x)=1+1/x-1/(x^2) is Maximum(2, 5/4)